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Robust Multiloop Controller Design of Uncertain Affine TFM(Transfer Function Matrix) System  

Byun Hwang-Woo (한양대학교 전기공학과)
Yang Hai-Won (한양대학교 전기공학과)
Publication Information
The Transactions of the Korean Institute of Electrical Engineers D / v.54, no.1, 2005 , pp. 17-25 More about this Journal
Abstract
This paper provides sufficient conditions for the robustness of Affine linear TFM(Transfer Function Matrix) MIMO (Multi-Input Multi-Output) uncertain systems based on Rosenbrock's DNA (Direct Nyquist Array). The parametric uncertainty is modeled through a Affine TFM MIMO description, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. For this type of parametric robust performance we show robustness of the Affine TFM systems using Nyquist diagram and GB, DNA(Direct Nyquist Array). Multiloop PI/PB controllers can be tuned by using a modified version of the Ziegler-Nickels (ZN) relations. Simulation examples show the performance and efficiency of the proposed multiloop design method.
Keywords
GBM(Gershgorin Band Method); Affine TFM(Transfer Function Matrix) MIMO(Multi-Input Multi-Output) system; Robustness; RM-PI/PID (Robust Multiloop-PI/PID); DNAM(Direct Nyquist Array Method);
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Times Cited By KSCI : 1  (Citation Analysis)
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1 W. L. Luyben, 'Getting More Information from Relay-Feedback Tests'. Ind. Eng. Chem. Res, vol. 40, pp. 4391-4402, 2001   DOI   ScienceOn
2 C. T. Baab, J. C. Cockburn, H. A. Latchman & O. D. Crisalle, 'Extension of the Nyquist Robust Margin to Systems with Nonconvex Value Sets', AACC, pp. 1414-1419, June 2001   DOI
3 M. Araki and O. I. Nwokah, 'Bounds for Closed-Loop Transfer Function of Multivariable Systems', IEEE Trans. on Automatic Control, vol. 20, pp. 666-670, 1975   DOI
4 W. K. Ho, O. P. Gn, E. B. Tay, & E. E. Ang, 'Performance and Gain and Phase Marins of Well-Known PID Tuning Formulas', IEEE Trans. on Control systems tech., vol. 4, pp. 473-477, 1996   DOI
5 T. E. Djaferis, Robust Control Design: A Polynomial Approach, Kluwer Academic Pub., 1995
6 J. Ackerman, Robust Control: Systems with Uncertain Physical Parameters, Springer-Verlag, 1993
7 Fu. M, 'Computing the frequency response of linear systems with parametric perturbations', System and Control Letters, vol. 15, pp. 45-52, 1990   DOI   ScienceOn
8 Rosenbrock H. H, State-Space and Multivariable Theory, London : U. K. Nelson, 1970
9 K. Glover, J. C. Doyle, 'State-space fomulate for all stabilizing controllers that satisfy an $H_{\infty}$-norm bound and relations to risk sensitivity', System and Control Letters, vol. 11, pp. 167-172, 1988   DOI   ScienceOn
10 W. K. Ho and Wen Xu, 'Multivariable PID Controller Design Based on the Direct Nyquist Array Method', Proc. of the American Control Con. Pennsylvania, pp. 3524-3528, 1998   DOI
11 C. H. Houpis, Quantitative Feedback Theory (QFT) Technique, CRC Press, pp. 701-717, 1996
12 V. L. Kharitonov, 'Asymptotic stability of an equilibrium position of a family of systems of linear differential equations', Differential'nye Uraveniya, vol. 14, pp. 1483-1485, 1978
13 Barmish. B. R., Hollot. C. V., Kraus. F., and Tempo. R., 'Extreme point results for robust stabilization of interval plants with first order compensators', IEEE Trans. on Automatic Control, vol. 37, pp. 707-714, 1992   DOI   ScienceOn
14 Ghosh. B, 'Some new results on the simultaneous stability of a family of single input, single output systems', System and Control Letters, vol. 6, no. 1, pp. 39-45, 1985   DOI   ScienceOn
15 Bartlett. A. C., Hollot C. V., and Huang. L., 'Root locations of an entire polytope of polynomials: it suffices to check the edges', Math. Control & Signals Sys., vol 1, pp. 61-71, 1988   DOI
16 S. P. Bhattacharyya et al 2, Robust Control: The Parametric Approach, Prentice-Hall, 1995
17 Birdwell. J, Castanon. D, Athans. M, 'On reliable control system designs with and without feedback reconfigurations', Proc. IEEE Conf. Control, pp. 419-426, Dec. 1979   DOI
18 Etfhymios. K & Neil. M, 'Extreme point solution to Diagonal dominance problem and Stability analysis of uncertain systems.', Proc. of the American Control Con., pp. 3936-3940, 1997   DOI
19 Saeks. R, Murray. J, 'Fractional representations, algebraic geometry and the simultaneous stabilization problem', IEEE Trans. on Automatic Control, vol. 27, pp. 895-903, 1982   DOI
20 G. Zames, 'Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses', IEEE Trans. on Automatic Control, vol. 26, no. 2, pp. 301-320, 1981   DOI
21 A. C. Bartlett, et al. 1, 'A necessary sufficient condition for schur invariance degeneralized stability of polytopes polynomials,' IEEE Trans. on Automatic Control, vol. 33, no. 6, pp. 575-583, 1988   DOI   ScienceOn